Library of Congress Cataloging-in-Publication Data
Martin, B. R. (Brian Robert)
Nuclear and particle physics/B. R. Martin.
p. cm.
ISBN-13: 978-0-470-01999-3 (HB)
ISBN-10: 0-470-01999-9 (HB)
ISBN-13: 978-0-470-02532-1 (pbk.)
ISBN-10: 0-470-02532-8 (pbk.)
1. Nuclear physics–Textbooks. 2. Particle physics–Textbooks. I. Title.
QC776.M34 2006
539.702–dc22
2005036437
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN-13 978-0 470 01999 9 (HB) ISBN-10 0 470 01999 9 (HB)
978-0 470 02532 8 (PB) 0 470 02532 8 (PB)
Contents
Preface xi
Notes xiii
Physical Constants and Conversion Factors xv
1 Basic Concepts 1
1.1 History 1
1.1.1 The origins of nuclear physics 1
1.1.2 The emergence of particle physics: the standard model and hadrons 4
1.2 Relativity and antiparticles 7
1.3 Symmetries and conservation laws 9
1.3.1 Parity 10
1.3.2 Charge conjugation 12
1.4 Interactions and Feynman diagrams 13
1.4.1 Interactions 13
1.4.2 Feynman diagrams 15
1.5 Particle exchange: forces and potentials 17
1.5.1 Range of forces 17
1.5.2 The Yukawa potential 19
1.6 Observable quantities: cross sections and decay rates 20
1.6.1 Amplitudes 21
1.6.2 Cross-sections 23
1.6.3 Unstable states 27
1.7 Units: length, mass and energy 29
Problems 30
2 Nuclear Phenomenology 33
2.1 Mass spectroscopy and binding energies 33
2.2 Nuclear shapes and sizes 37
2.2.1 Charge distribution 37
2.2.2 Matter distribution 42
2.3 Nuclear instability 45
2.4 Radioactive decay 47
2.5 Semi-empirical mass formula: the liquid drop model 50
2.6 -decay phenomenology 55
2.6.1 Odd-mass nuclei 55
2.6.2 Even-mass nuclei 58
2.7 Fission 59
2.8 -decays 62
2.9 Nuclear reactions 62
Problems 67
3 Particle Phenomenology 71
3.1 Leptons 71
3.1.1 Lepton multiplets and lepton numbers 71
3.1.2 Neutrinos 74
3.1.3 Neutrino mixing and oscillations 76
3.1.4 Neutrino masses 79
3.1.5 Universal lepton interactions – the number of neutrinos 84
3.2 Quarks 86
3.2.1 Evidence for quarks 86
3.2.2 Quark generations and quark numbers 89
3.3 Hadrons 92
3.3.1 Flavour independence and charge multiplets 92
3.3.2 Quark model spectroscopy 96
3.3.3 Hadron masses and magnetic moments 102
Problems 108
4 Experimental Methods 111
4.1 Overview 111
4.2 Accelerators and beams 113
4.2.1 DC accelerators 113
4.2.2 AC accelerators 115
4.2.3 Neutral and unstable particle beams 122
4.3 Particle interactions with matter 123
4.3.1 Short-range interactions with nuclei 123
4.3.2 Ionization energy losses 125
4.3.3 Radiation energy losses 128
4.3.4 Interactions of photons in matter 129
4.4 Particle detectors 131
4.4.1 Gas detectors 131
4.4.2 Scintillation counters 137
4.4.3 Semiconductor detectors 138
4.4.4 Particle identification 139
4.4.5 Calorimeters 142
4.5 Layered detectors 145
Problems 148
5 Quark Dynamics: the Strong Interaction 151
5.1 Colour 151
5.2 Quantum chromodynamics (QCD) 153
5.3 Heavy quark bound states 156
5.4 The strong coupling constant and asymptotic freedom 160
5.5 Jets and gluons 164
5.6 Colour counting 166
5.7 Deep inelastic scattering and nucleon structure 168
Problems 177
6 Electroweak Interactions 181
6.1 Charged and neutral currents 181
6.2 Symmetries of the weak interaction 182
6.3 Spin structure of the weak interactions 186
6.3.1 Neutrinos 187
6.3.2 Particles with mass: chirality 189
6.4 W and Z0 bosons 192
6.5 Weak interactions of hadrons 194
6.5.1 Semileptonic decays 194
6.5.2 Neutrino scattering 198
6.6 Neutral meson decays 201
6.6.1 CP violation 202
6.6.2 Flavour oscillations 206
6.7 Neutral currents and the unified theory 208
Problems 213
7 Models and Theories of Nuclear Physics 217
7.1 The nucleon – nucleon potential 217
7.2 Fermi gas model 220
7.3 Shell model 223
7.3.1 Shell structure of atoms 223
7.3.2 Nuclear magic numbers 225
7.3.3 Spins, parities and magnetic dipole moments 228
7.3.4 Excited states 230
7.4 Non-spherical nuclei 232
7.4.1 Electric quadrupole moments 232
7.4.2 Collective model 236
7.5 Summary of nuclear structure models 236
7.6 -decay 238
7.7 -decay 242
7.7.1 Fermi theory 242
7.7.2 Electron momentum distribution 244
7.7.3 Kurie plots and the neutrino mass 246
7.8 -emission and internal conversion 248
7.8.1 Selection rules 248
7.8.2 Transition rates 250
Problems 252
8 Applications of Nuclear Physics 255
8.1 Fission 255
8.1.1 Induced fission – fissile materials 255
8.1.2 Fission chain reactions 258
8.1.3 Nuclear power reactors 260
8.2 Fusion 266
8.2.1 Coulomb barrier 266
8.2.2 Stellar fusion 267
8.2.3 Fusion reaction rates 270
8.2.4 Fusion reactors 273
8.3 Biomedical applications 278
8.3.1 Biological effects of radiation: radiation therapy 278
8.3.2 Medical imaging using radiation 282
8.3.3 Magnetic resonance imaging 290
Problems 294
9 Outstanding Questions and Future Prospects 297
9.1 Particle physics 297
9.1.1 The Higgs boson 297
9.1.2 Grand unification 300
9.1.3 Supersymmetry 304
9.1.4 Particle astrophysics 307
9.2 Nuclear physics 315
9.2.1 The structure of hadrons and nuclei 316
9.2.2 Quark–gluon plasma, astrophysics and cosmology 320
9.2.3 Symmetries and the standard model 323
9.2.4 Nuclear medicine 324
9.2.5 Power production and nuclear waste 326
Appendix A: Some Results in Quantum Mechanics 331
A.1 Barrier penetration 331
A.2 Density of states 333
A.3 Perturbation theory and the Second Golden Rule 335
Appendix B: Relativistic Kinematics 339
B.1 Lorentz transformations and four-vectors 339
B.2 Frames of reference 341
B.3 Invariants 344
Problems 345
Appendix C: Rutherford Scattering 349
C.1 Classical physics 349
C.2 Quantum mechanics 352
Problems 354
Appendix D: Solutions to Problems 355
References 393
Bibliography 397
Index 401
Preface
It is common practice to teach nuclear physics and particle physics together in an
introductory course and it is for such a course that this book has been written. The
material is presented so that different selections can be made for a short course of
about 25–30 lectures depending on the lecturer’s preferences and the students’
backgrounds. On the latter, students should have taken a first course in quantum
physics, covering the traditional topics in non-relativistic quantum mechanics and
atomic physics. A few lectures on relativistic kinematics would also be useful, but
this is not essential as the necessary background is given in appendix B and is only
used in a few places in the book. I have not tried to be rigorous, or present proofs
of all the statements in the text. Rather, I have taken the view that it is more
important that students see an overview of the subject which for many – possibly
the majority – will be the only time they study nuclear and particle physics. For
future specialists, the details will form part of more advanced courses. Nevertheless,
space restrictions have still meant that it has been necessary to make a
choice of topics covered and doubtless other, equally valid, choices could have
been made. This is particularly true in Chapter 8, which deals with applications of
nuclear physics, where I have chosen just three major areas to discuss. Nuclear and
particle physics have been, and still are, very important parts of the entire subject
of physics and its practitioners have won an impressive number of Nobel Prizes.
For historical interest, I have noted in the footnotes many of the awards for work
related to the field.
Some parts of the book dealing with particle physics owe much to a previous book,
Particle Physics, written with Graham Shaw of Manchester University, and I am
grateful to him and the publisher, JohnWiley and Sons, for permission to adapt some
of thatmaterial for use here. I also thankColinWilkin for comments on all the chapters
of the book, David Miller and Peter Hobson for comments on Chapter 4 and Bob
Speller for comments on the medical physics section of Chapter 8. If errors or
misunderstandings still remain (and any such are of course due tomealone) Iwould be
grateful to hear about them. I have set up a website (www.hep.ucl.ac.uk/ brm/
npbook.html) where I will post any corrections and comments.
Brian R. Martin
January 2006
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